WASHINGTON — President Trump’s commission on voter fraud, which has ricocheted between controversies since its creation in May, is scheduled to hold its second public meeting on Tuesday in New Hampshire. Already, the commission’s de facto leader has warmed up for the session by suggesting that the election in November of Senator Maggie Hassan, a New Hampshire Democrat, was rigged.

The accusation led the state’s entire congressional delegation to demand that William M. Gardner, the New Hampshire secretary of state, resign from the commission. Mr. Gardner, a Democrat and the host of the meeting on Tuesday, refused to do so, and said the state’s two senators and two representatives were being hypocritical.

Uproar has become standard practice for the fraud panel, officially called the Presidential Advisory Commission on Election Integrity. Critics say the commission is a pretext for Republican efforts to make it harder to register and to vote, and that it will reach a predetermined conclusion, that tough new rules are needed to prevent fraud. Studies have repeatedly shown that illegal voting is very rare, and that voter impersonation — perhaps the main danger suggested by advocates of tighter election rules — is next to nonexistent.

Since its formation, the commission has been accused of skirting open-government laws; it has publicly released personal details like street and e-mail addresses of citizens who contacted it, almost always to complain; and generated a fierce backlash when it asked state election officials to turn over data on every voter in the United States. The advocacy group Common Cause states in a new report that the request led more than 5,000 Colorado voters to de-register so that their personal information would not be sent to Washington.

In an interview, Mr. Gardner said the serial controversies had unfairly sullied the commission’s public image almost before it had begun work, adding that he had been branded by some as a vote suppressor merely by serving on it.

“You don’t judge a book by its cover,” he said. “You judge at the end.”

The Tuesday meeting will be devoted to studying declining public confidence in elections, one of the mandates given the panel by Mr. Trump, who has claimed without foundation that millions of fraudulent ballots enabled Hillary Clinton to win the popular vote in November. Mr. Gardner said he did not necessarily favor imposing new qualifications for registering and voting, but he added that when burdens like poll taxes and literacy tests were imposed on citizens and registering often required a trip to the local courthouse, voter turnout was far higher than it is now.

The meeting will include a statistical review of decades of elections and a discussion of whether fraud has reduced citizens’ trust in the fairness of elections — a timely topic, as an allegation of fraud in New Hampshire by one of the commission’s leading members have dominated the runup to the session.

Image

The secretary of state of New Hampshire, William M. Gardner, right, (shown in 2012) has come under criticism for suggestions of voter fraud in the state.CreditJim Cole/Associated Press

The charge was leveled on Thursday by Kris Kobach, the Republican secretary of state in Kansas, the commission’s vice chairman and, most recently, columnist for the far-right website Breitbart News. In his debut column, Mr. Kobach said Ms. Hassan’s victory in the contest for a New Hampshire seat in the Senate — and perhaps Mrs. Clinton’s narrow win in the state — likely were the result of voter fraud.

His accusation was based on data from Mr. Gardner’s office showing that 6,540 people in New Hampshire registered to vote on Election Day using out-of-state driver’s licenses to verify their identities, but only 1,014 of the registrants later obtained a New Hampshire license.

Mr. Kobach said that was evidence that the remaining 5,313 registrants were illegal voters from other states — enough voters, he noted, to supply the narrow margins of victory for both Ms. Hassen and Mrs. Clinton.

“If the presidential election had been closer and had come down to a margin of three or four electoral college votes, then this voter fraud might have had extraordinary consequences,” he wrote. “Regardless, in the Senate, it is highly likely that voting by nonresidents changed the result.”

Voting-rights advocates were contemptuous.

In an online article titled “Kobach Discovers College Students Live in College Towns,” the Brennan Center for Justice at New York University said the bulk of the registrations very likely were filed by out-of-state college students who chose to vote in New Hampshire instead of their home states, as the law allows.

Excluding community colleges, New Hampshire is home to more than 34,000 college and university students. According to New Hampshire Public Radio, the places where registrants most frequently displayed out-of-state licenses were all college towns.

“It’s not the first time that Kris Kobach has mischaracterized evidence to legitimize an otherwise fraudulent claim of voter fraud,” Vanita Gupta, president of the Leadership Conference on Civil and Human Rights, said. “But he’s now in a position where the consequences of doing this are really serious.”

Mr. Kobach’s allegation sparked an immediate demand by the state’s four legislators in Congress that Mr. Gardner resign from the commission. In a broadcast interview on Thursday, Mr. Gardner called that hypocritical, asking whether any of the legislators had ever quit a congressional committee because they disagreed with the views of another member.

“There is no proof that there is any voter fraud,” he said on Friday, but “people have a right to their opinions.”

A version of this article appears in print on , on Page A16 of the New York edition with the headline: Anger Follows an Accusation of Voter Fraud. Order Reprints | Today’s Paper | Subscribe